MOLYBDENUM PERMALLOY FOR INDUCTANCE COILS 405 



When the core permeability ix is reduced by dilution of a given 

 material, the hysteresis and residual loss coefficients a and c vary so 

 as to make the products ixc = ki and fxa — ki approximately constant, 

 as may be seen by reference to Table I. The core loss resistance in 

 ohms at frequency /cycles per second may therefore be expressed with 

 reasonable accuracy as 



(6) Rm = Lfikr + k^Bm + fief) =Lf(k,-\- ^^ + ^ef) , 



where the eddy current coefficient e depends upon the particle diameter 

 /, and the alloy resistivity p being proportional ^^ to t^/p. 

 The coil quality factor is thus 



(7) n = '^'^^^ - ^^-^ 



Re + R„ 19p, X 109 >. / - lOmTT 



Sfjid^ 



+ f{h+'^ + ,ej) 



Case I: If the value of m is fixed and d and Re can be freely chosen, 

 it is desirable to know the value of n which will yield the highest 

 possible value of Q. By substituting in (7) the value of d"^ obtained 

 from (5) and setting the derivative with respect to ^ equal to zero, the 

 following is obtained for the optimum permeability : 



fr.. , ,^8 _ 52.5 X lO^Vm^ 



The corresponding values of d and Re can be obtained from equations 

 (5) and (2). The corresponding value of Q, which is the greatest 

 obtainable under these conditions is 



(9) (3'n.ax = 



— + y + 5M^/ 



If a smaller value of Q than that obtained from (9) is acceptable, 

 equations (7) and (5) can be solved simultaneously for d and fx. A 

 smaller value of n than that obtained from (8) and a correspondingly 

 smaller value of d will result. 



Case II: If modulation is unimportant and the hysteresis loss re- 

 sistance is negligible in comparison with other component losses, then 

 d and ju can be selected without regard to modulation. Equation (7) 

 can be differentiated directly and solved for the permeability required 

 to yield the maximum value of Q. This optimum permeability is 



(■\(\\ ( //\o 19pc X lU 



^^^^ ^^ ^" = sedT ' 



